An estimate of the

Context. Increasing our knowledge of the interior structure, composition, and density distribution of exoplanets is crucial to make progress in the understanding of exoplanetary formation, migration and habitability. However, the directly measurable mass and radius values offer little constraint on interior structure, because the inverse problem is highly degenerate. Therefore, there is a clear need for a third observable of exoplanet interiors. This third observable can be the k2 fluid Love number which measures the central mass concentration of an exoplanet. Aims. The aims of this paper are (i) to develop a basic model to fit the long-term radial velocity and TTV variations caused by tidal interactions, (ii) to apply the model to the WASP-18Ab system, and (iii) to estimate the Love number of the planet. Methods. Archival radial velocity, transit and occultation timing data were collected and fitted using the model introduced here. Results. The best model fit to the archival radial velocity and timing data of WASP-18Ab was obtained with a Love number of the massive (~10 MJup) hot Jupiter WASP-18Ab: $k_{2,\textrm{Love}}\,{=}\,0.62^{+0.55}_{-0.19}$. This causes apsidal motion in the system, at a rate of ~0.0087 ± 0.0033°∕days ≊ 31.3 ± 11.8 arcsec day−1. When checking possible causes of periastron precession, other than the relativistic term or the non-spherical shape of the components, we found a companion star to the WASP-18 system, named WASP-18B which is a probable M6.5V dwarf with ~0.1 M⊙ at 3519 AU distance from the transit host star. We also find that small orbital eccentricities may be real, rather than an apparent effect caused by the non-spherical stellar shape